The cost of car, purchased 2 years ago, depreciates at the rate of $20 %$ every year. If its present worth is ₹ 315600, find its purchase price.

₹ 493,125

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₹ 493,175

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₹ 493,525

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₹ 496,725

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Solution

The correct option is A
₹ 493,125

Here, V = present value = ₹ 315,600, n = 2 years, r = $20 %$ ,

Let, $V_{0}$ = Purchase price

Using $V = V_{0} {(1 - \frac{r}{100})}^{n},$
$315, 600 = V_{0} {(1 - \frac{20}{100})}^{2} o r, 315, 600 = V_{0} {(\frac{80}{100})}^{2} = V_{0} (\frac{16}{25}) o r, V_{0} = 315, 600 \times \frac{25}{16} = ₹ 493, 125$

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The cost of car, purchased 2 years ago, depreciates at the rate of 20% every year. If its present worth is ₹ 315600, find its purchase price.

The correct option is A ₹ 493,125 Here, V = present value = ₹ 315,600, n = 2 years, r = 20%, Let, V0 = Purchase price Using V=V0(1−r100)n, 315,600=V0(1−20100)2or, 315,600=V0(80100)2=V0(1625)or, V0=315,600×2516=₹493,125

The cost of car, purchased 2 years ago, depreciates at the rate of $20 %$ every year. If its present worth is ₹ 315600, find its purchase price.